Using this info given in image. Please solve the question.

Tollowing Trequency distribution Of observea Trequencies. Xi o N 11 w w O #In our ahcarved data wa did not not any draw of A hearte Hanra For problems (5), (6) and (7), I will grade you only on your final answer. You do not need to show work. Round all your numbers to 3 decimals For the remaining problems, let P1 = 01/20 and p2 = 02/20 5) Suppose the fraction of students at university 1 who took statistics is given by p1- Suppose the fraction of students at university 2 who took statistics is given by p2. You survey 10 people from each university (so 20 people total). (a) What is the probability that more than half of the surveyed students took statistics from university 1? (b) What is the probability that more than half of the surveyed students took statistics from university 2? (c) Assuming that the universities are independent, what is the probability that more than half of the surveyed students took statistics from university 1 and more than half of the surveyed students took statistics from university 2? (d) Assuming that the universities are independent, what is the probability that more than half of the surveyed students took statistics from university 1 or more than half of the surveyed students took statistics from university 2? (6) Now suppose you redo your survey of university 1, but you haven't decided how many students to ask, so you just keep asking students indefinitely. (a) What is the probability that none of the first 3 people have taken statistics? b) What is the probability that the first person you find who takes statistics is the 5th person you ask? (c) What is the probability that the first person you find who takes statistics is the 5th person you ask, given that none of the first 3 people have taken statistics? 7) Now we will play a game. Let a = p1 and b = 3/p2 . Our game will have the following steps: . You start with $100 You roll a regular six-sided die: 1 or 2 I multiply your money by a 3 or 4 I take all your money 5 or 6 I multiply your money by b . With whatever money you have left, we repeat step (2) one more time . Then we stop Find the expected amount of money you will have at the end of this game